The vast majority of speaker embedding networks use the statistical pooling layer introduced by x-vectors, i.e. mean and standard deviation (std) for each frequency and channel combination [1]}. The main family of alternative pooling methods enhance these statistics with an attention mechanism. Examples are single and multi-head attention, as well as Net and Ghost-VLAD [2]}, [3]}, [4]}. Both attention and VLAD methods employ a set of heads (i.e. trainable network parameters which are broadly analogous to the means of a mixture model) to cluster the output features into broad phonetic categories in an unsupervised and end-to-end fashion. The resulting statistical pooling is defined as the concatenation of the per-head statistics. Their main difference lies in the normalization; the attention normalizes only over the time axis while the VLAD over the attentive heads. Second order statistics (i.e. std features) may also be added as in the case of average pooling. More recent approaches exist, such as vector-based attentive pooling [5]}, phonetically-aware attention [6]}, and cross-attention [7]}.
